Solve 9c^4-81a^2

$$9 c ^ { 4 } - 81 a ^ { 2 }$$

Factor

$$9\left(c^{2}-3a\right)\left(3a+c^{2}\right)$$

Solution Steps

Factor out 9.

$$9\left(c^{4}-9a^{2}\right)$$

Consider c^{4}-9a^{2}. Rewrite c^{4}-9a^{2} as \left(c^{2}\right)^{2}-\left(3a\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(c^{2}-3a\right)\left(c^{2}+3a\right)$$

Reorder the terms.

$$\left(-3a+c^{2}\right)\left(3a+c^{2}\right)$$

Rewrite the complete factored expression.

$$9\left(-3a+c^{2}\right)\left(3a+c^{2}\right)$$

Evaluate

$$9\left(c^{4}-9a^{2}\right)$$